2015/06/29 by Martin Bauer, Martins Bruveris, Bauer, Martin +5
Computer Science · Engineering · #58B20 (Primary) #62H25 #62H30 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics #Image Processing and 3D Reconstruction #Medical Image Segmentation Techniques #Medical Imaging and Analysis #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1506.08840
openalex publication_date 2015/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the recent years, Riemannian shape analysis of curves and surfaces has found several applications in medical image analysis. In this paper we present a numerical discretization of second order Sobolev metrics on the space of regular curves in Euclidean space. This class of metrics has several desirable mathematical properties. We propose numerical solutions for the initial and boundary value problems of finding geodesics. These two methods are combined in a Riemannian gradient-based optimization scheme to compute the Karcher mean. We apply this to a study of the shape variation in HeLa cell nuclei and cycles of cardiac deformations, by computing means and principal modes of variations.